Titebond Original would be a good choice for this job. You will still need to get the gluing surfaces as clean as possible.

While I am a firm believer in hide glue, and use it for most of my bridge jobs, it is not a good choice 1] on surfaces that have been previously glued with an unknown synthetic glue unless all the old glue can be removed from the pores, 2] for someone who is not tooled up to get the joint clamped within 1 minute of when the glue is applied, and 3] someone who has not been trained to use it.

The exception is if you want to use this job as a learning tool, don't mind making inside and outside clamping cauls for the job, and are willing to have the joint fail 2 or 3 times before you get it right.

As John said, a bridge doctor is designed to counter-act a severely warped top. It will not improve a glue joint.

Chris's 5 step instructions describe the basics you need to know. In addition to cleaning off the old glue, you'll need to scrape off any finish that might be covering part of the gluing surface, which may be the reason the joint failed in the first place. If you use a clothes iron or heat lamp, you have to protect the top from the heat with a cardboard or wooden shield, preferably with aluminum foil on the outside surface. Instead, I use a 1" x 5" 25 watt heat blanket, available from McMaster-Carr or MSC Industrial Supply and plug it into a Harbor Freight router controller to control the temperature. That way, I can apply the heat exactly where I want it, and it's half the price of the LMI rig. I drill two tiny holes in the saddle slot and use small brads for alignment pins to keep everything in position during the gluing process. I have two holes drilled in my outside caul to accommodate the pins, and remove them after the glue has set.